Question: In a study of depression among college students, 182 undergraduates at a rural mid-size southeastern university were recruited. Participants completed a battery of psychological tests and provided demographic information. One question asked was, "Have you ever experienced the following symptoms for a period of two or more consecutive weeks: sadness, concentration problems, fatigue, sleep, or appetite problems?" A total of 79 participants responded "yes" to this question and were classified as ever having depressive symptoms; the remaining 103 responded "no". (Source: Counseling & Clinical Psychology Journal, May 2006, vol. 3 p.60-70)

1. (4 pts) What is the estimate of the percentage of college students at this university who have ever had depressive symptoms based on these data?
2. (8 pts) Experts contend that 1 in 5 people will experience depressive symptoms over the course of their lifetime. Perform the appropriate statistical test to determine whether the proportion of college students who have experienced depressive symptoms is significantly different from 1 in 5 (i.e., 20%). You must write out all steps of the test (calculations may be done using Stata) and write a sentence summarizing the result of the test.

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